Abstract

We present an experimental method for directly observing the amplification of microscopic intrinsic noise in a high-dimensional chaotic laser system, a laser with delayed feedback. In the experiment, the chaotic laser system is repeatedly switched from a stable lasing state to a chaotic state, and the time evolution of an ensemble of chaotic states starting from the same initial state is measured. It is experimentally demonstrated that intrinsic noises amplified by the chaotic dynamics are transformed into macroscopic fluctuating signals, and the probability density of the output light intensity actually converges to a natural invariant probability density in a strongly chaotic regime. Moreover, with the experimental method, we discuss the application of the chaotic laser systems to physical random bit generators. It is experimentally shown that the convergence to the invariant density plays an important role in nondeterministic random bit generation, which could be desirable for future ultimate secure communication systems.

Received 15 April 2012Accepted 10 September 2012Published online 21 December 2012

Lead Paragraph: In real physical systems, there always exists microscopic noise, and the system is randomly perturbed. If the deterministic part of its system is strongly chaotic, an initial uncertainty due to the noise is rapidly amplified by the dynamics so that macroscopic observables will be unpredictable after long time. In such dynamical systems, an invariant probability distribution is fundamental and it plays an important role in characterizing the long time behaviors and the statistical properties of the systems.1 The convergence rate to the invariant distribution is also an important feature, and it is deeply related to statistical properties of nonequilibrium systems.2–5 So far, there have been many mathematical and numerical studies on the fundamental statistical properties of strongly chaotic dynamical systems. However, the experimental investigation of the statistical properties has not yet been done in detail on the basis of the direct observation of a noise amplification effect in strongly chaotic systems. In this article, we experimentally study the statistical properties of the noise amplification in a laser system with delayed feedback, by actually observing the convergence to an invariant probability distribution of the observable. Moreover, the application of the noise amplification effect by the chaotic dynamics to nondeterministic random bit generation is discussed. It is experimentally shown that nondeterministic random bit generation is possible if the sampling time interval of the observable is much longer than the time needed for the convergence to the natural invariant probability distribution.